I've had a thorough look at the Modern Defence (1.e4 e5 2.f4 exf4 3.Nf3 d5) and four of the minor defences (3...h5, 3...Nf6, 3...Ne7 and 3...Be7), of which the Cunningham Defence, 3...Be7, appears to be the most important by a fair margin, though 3...Ne7 is interesting and may not be significantly inferior.
I am yet to post the games and analysis up on my Weebly site- I intend to upload games and analysis of these lines, plus the King's Bishop Gambit (3.Bc4) and Mason Gambit (3.Nc3) in bulk. I am currently moving over to looking at the latter two third moves.
Anyway, I'll start off with a summary of my main conclusions regarding the Modern Defence.
Modern Defence (3.Nf3 d5)
3...d5 appears to be a perfectly reasonable response for those who would rather avoid the complications of the lines that I've been through earlier, involving holding onto the f4-pawn with ...g7-g5. Unlike many other such declining lines in the Open Games, it tends not to lead to sterility- in most lines there are enough imbalances left in the position to provide good scope for both sides to play for a win. However, also unlike most other such declining lines, it doesn't generally score quite as well as holding onto the pawn (3...d5 is scoring 47% in the Chesslive.de database while 3...g5 is scoring an impressive 53%).
I'd say that the choice appears to be a matter of taste, it's really down to how comfortable one feels as Black in the resulting positions.
After 4.exd5 Nf6 (4...Qxd5 is playable, but not as reliable- 5.Nc3 Qe6+ 6.Be2 Bd6 7.0-0 is one good response, while 5.d4 was played successfully in a couple of high-level games including V.Zvjaginsev-Wang Hao, Taiyuan 2007) White then has a choice.
A) 5.c4 is fairly unusual but appears good enough for dynamic equality- White generally gets the better pawn structure but Black ends up with superior piece activity and some kingside attacking chances. Most popular is 5...c6 which is scoring a healthy 50% for Black. Magnus Carlsen tried 5.c4 with success in a 2012 blitz game against Nikoly Chadaev.
B) 5.Bb5+ is most popular, and generally produces the same result- White has the better pawn structure but Black has the majority of the piece play and attacking chances, and in practice Black is doing very well. In H.Nakamura-A.Kosteniuk, Kings vs Queens 2011, Black replied with the inferior 5...Nbd7 and ended up worse, but after the superior 5...c6 6.dxc6 Nxc6, Black is scoring 59%. InV.Zvjaginsev-A.Kunte, World Cup 2007, play continued 7.d4 Qa5+ which should have led to a slight advantage for White, but after 7...Bd6 defending f4, Black has good chances.
C) 5.Bc4 is the best practical chance, scoring a respectable 54% for White in the Chesslive.de database, for in this line it tends to be White who gets the majority of the piece play and attacking chances, while Black tends to rely upon the f4-pawn to provide nuisance value.
One recent stunbling block that has emerged for 5.Bc4 is the continuation 5...Nxd5 6.0-0 Be6 (6...Be7 7.Bxd5!? Qxd5 8.Nc3 worked out well for White in M.Carlsen-Wang Yue, Bazna Kings 2010, relying upon development and open lines to compensate for Black's bishop-pair) 7.Bb3 (7.Bxd5 Bxd5 8.d4 Be7 9.Bxf4 is still playable, but less promising than when White brings Black's queen out into the open) 7...c5.
This featured in a high-profile encounter between Hikaru Nakamura and Mickey Adams, London Classic 2011. Play continued 8.Kh1 Nc6 9.d4 c4 10.Ba4 Bd6 and Black got the upper hand. White won, but only after Black squandered an opportunity to secure a large, probably winning, advantage at move 35 (35...b3!)
8.d4 is not very appealing for White after 8...cxd4 9.Nxd4 Bc5, setting up an irritating pin on the d4-knight, and Black is comfortable after, say, 10.Kh1 Bxd4 11.Qxd4 0-0.
However, White has two reasonable alternatives, 8.c4 (this blocks in White's bishop for now, but White can redeploy it to c2, with ideas of a kingside offensive), and 8.d3, both of which deal with Black's threat of ...c5-c4. 8.d3 Nc6 9.Bxd5 Bxd5 10.Bxf4 is OK for White, since White's play down the e and f-files offsets Black's bishop-pair. 8.c4 Nf6 9.d4 cxd4 10.Bxf4 is another sample line, with equal chances.
Another double-edged possibility in Nakamura's game was 10.Bc4!?, with the idea of sacrificing an exchange following 10...Ne3 10.Bxe3 Bxc4 12.Bxf4 Bxf1 13.Qxf1. I'm not convinced that White's compensation is sufficient after 13...Bd6, but it would have been a better try for White than the 10.Ba4 played in the game.
In conclusion, the Modern Defence is currently looking OK for both sides. Despite the problem line that Nakamura encountered above, I still think that White's best bet is the line 4.exd5 Nf6 5.Bc4.